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Recurrent neural networks (RNNs) are powerful architectures to model sequential data, due to their capability to learn short and long-term dependencies between the basic elements of a sequence. Nonetheless, popular tasks such as speech or…

This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…

Multi-focus color image fusion refers to integrating multiple partially focused color images to create a single all-in-focus color image. However, existing methods struggle with complex real-world scenarios due to limitations in handling…

The field of neural networks has seen significant advances in recent years with the development of deep and convolutional neural networks. Although many of the current works address real-valued models, recent studies reveal that neural…

In this paper, we propose a Sparse Low-rank Quaternion Approximation (SLRQA) model for color image processing problems with noisy observations. %Different from the existing color image processing models, The proposed SLRQA is a quaternion…

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Remotely sensed images may contain some missing areas because of poor weather conditions and sensor failure. Information of those areas may play an important role in the interpretation of multitemporal remotely sensed data. The paper aims…

Recently, quaternion collaborative representation-based classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among…

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm…

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional data. A well-known method for TR decomposition is the alternating…

Moving target detection is a challenging computer vision task aimed at generating accurate segmentation maps in diverse in-the-wild color videos captured by static cameras. If backgrounds and targets can be simultaneously extracted and…

Reduced biquaternion (RB), as a four-dimensional algebra highly suitable for representing color pixels, has recently garnered significant attention from numerous scholars. In this paper, for color image processing problems, we introduce a…

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…

We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…

In this paper a quaternion approach of enhancement method is proposed in which color in the image is considered as a single entity. This new method is referred as the alpha-rooting method of color image enhancement by the two-dimensional…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…